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The goal of this research was to design and develop a framework to effectively utilise GBSAR interferometry for deformation monitoring applications. A range of aspects of GBSAR interferometry has been involved. This section summarises the main research outcomes from this project, as follows:

1. Non-local “MIAS” method.

A simple but efficient similarity measure has been presented to identify resembling pixels for distributed scatterers, together with a comprehensive non-local “MIAS” method based upon this concept, which is able to accurately estimate coherence and interferometric phase. “MIAS” can largely mitigate the coherence estimation bias and avoid overestimating the decorrelated area without the cost of the spatial resolution.

2. Selection of (partially) coherent pixels.

A full-rank criterion for the selection of coherent pixels from a redundant network of interferograms has been developed, which enables the selection of not only qualified partially coherent pixels, but also all persistent scatterers. The proposed method makes the most of redundant observations and allows an adjustment to obtain a reliable value for the unknown. Finally, a reliable solution can be achieved in the InSAR time series analysis.

3. RT-GBSAR.

A novel processing chain (i.e. RT-GBSAR) for continuous GBSAR deformation monitoring has been demonstrated on the basis of the SBAS time series concept. The SBAS procedure in RT- GBSAR integrates the non-local “MIAS” method and the presented coherent pixel selection approach. RT-GBSAR processes continuous GBSAR images on a unit by unit basis. Significant issues in processing continuous GBSAR data (including the delay of displacement maps, the extreme cost of computational memory, and the loss of temporal evolution in the simultaneous processing of all data together) have been addressed by the proposed RT-GBSAR chain with three notable features: (i) low requirement of computational memory; (ii) insights into the temporal evolution of surface movements through temporally-coherent pixels; and (iii) real-

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time capability for processing an infinite number of images. 4. MC-GBSAR.

A new interferometric processing chain (i.e. MC-GBSAR) has been proposed for discontinuous GBSAR deformation monitoring, in which repositioning errors often occur in repeated campaigns and cause inaccuracies in interferometric observations. In this processing chain, GBSAR imagery can be automatically co-registered through amplitude-based feature matching with sub-pixel precision. By analysing the characteristics and effects of the typical errors (including atmospheric and repositioning errors) in GBSAR interferometry from its fundamental geometry, a new model has been developed and integrated into this chain for the combined correction of these errors. Based on experiments using both synthetic and real-world GBSAR data, it was found that greater repositioning errors always lead to less reliable displacement determination. With moderate effort in hardware deployment, the MC-GBSAR chain will potentially facilitate a range of deformation monitoring applications, especially in slow-changing scenarios. The MC-GBSAR chain can be a complementary tool to the RT- GBSAR chain for processing GBSAR data collected from all operation modes.

5. Deformation monitoring applications.

The presented algorithms and processing chains have been fully implemented and integrated into an in-house GBSAR data processing package (see Appendix B), making it a versatile tool for GBSAR deformation monitoring. Using this package, four deformation monitoring applications have been undertaken, including three continuous (a dune, a bridge, and a coastal cliff) and one discontinuous (a hillside) scenarios. The results were verified quantitatively via a defined precision indicator for the time series estimation and validated qualitatively via a priori knowledge of these observing sites. These successful applications have demonstrated the feasibility and effectiveness of the presented algorithms and chains for reliable, high-precision GBSAR deformation monitoring.

In the application of monitoring a fast-changing sand dune, observed movement took place only in areas devoid of vegetation while the area with sparse vegetation coverage remained stable over a short observing period of 1 hour 20 minutes, which suggests that the preservation of vegetation in the dune area plays an important role in stabilising the surface against sand motion. The application of monitoring the Queen Elizabeth II Metro Bridge showed that the bridge

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superstructure vibrated with a few millimetres of deflection when a train crossed it. It presents the feasibility of GBSAR interferometry for measuring rapid structural deformation.

In the application of monitoring the cliff on the north side of Tynemouth Priory and Castle, displacement maps reveal deformation signals only at locations near the sea. Time-series displacements, cumulative displacement maps, and relevant analysis suggest that the triggering of ground deformation is related to sea tides.

In the discontinuous monitoring of the southern hillside of Tynemouth Priory and Castle, two GBSAR campaigns were processed by the MC-GBSAR chain with and without co-registration processing, using both modelling and filtering approaches for the correction of atmospheric and geometric errors. The achieved results with respect to the two situations were consistent with each other. Finally, no significant movement was detected on the hillside over the observing period of two hours, presenting an anticipated result.

On the basis of these successful applications, it is fair to conclude that the research outcomes from this project will facilitate a range of deformation monitoring applications to which GBSAR is potentially suited.

7.2 Revisiting research objectives

This research aimed to design and develop a framework to effectively utilise GBSAR

interferometry for deformation monitoring applications. The research emphasizes the

performance of InSAR techniques in terms of accuracy, robustness, and real-time capability. The aim has been achieved through the accomplishment of the original four objectives as follows:

1. To evaluate the suitability and, where necessary, make necessary improvement to current fundamental InSAR techniques and advanced time series analysis algorithms for processing GBSAR imagery.

This has been addressed in Chapters 3 and 4, corresponding to research outcomes 1, 2 and 4 (in part). The non-local “MIAS” method overcomes the limitations in the conventional algorithms and achieves accurate coherence estimation and phase filtering. The new approach to selecting coherent pixels based on the full-rank criterion is able to maximise the density of selected pixels and optimise the reliability of GBSAR time series analysis by making the most of coherent

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phase redundancies. The atmospheric and repositioning errors in GBSAR interferometry have been investigated and a new model has been proposed for the correction of these errors.

2. To develop a (near-) real-time processing procedure with high degree of automation for a current FastGBSAR instrument to minimise delay after each data acquisition and to maximise the precision and reliability of the output deformation maps.

This has been addressed in Chapter 5, corresponding to research outcome 3: the novel RT- GBSAR processing chain for continuous GBSAR deformation monitoring. The real-time capability of RT-GBSAR was evaluated in Chapter 5 and successful applications have demonstrated that sub-millimetre measurement precision can be achieved in the time series estimation aspects of the RT-GBSAR chain.

3. To develop a discontinuous GBSAR procedure as a complementary module to the continuous pipeline for a complete GBSAR interferometry framework.

This has been addressed in Chapter 6, corresponding to research outcome 4: a new interferometric processing chain, MC-GBSAR, for discontinuous GBSAR deformation monitoring. MC-GBSAR has integrated the automatic co-registration of GBSAR images and the correction of atmospheric and repositioning errors between repeated campaigns. With moderate effort on hardware deployment in practice, MC-GBSAR can be a complementary tool to RT-GBSAR for a complete GBSAR interferometry framework.

4. To establish case studies to demonstrate the feasibility of the developed GBSAR data processing software system for a range of deformation monitoring applications to which GBSAR is suited.

Multiple applications have been completed in Chapters 4, 5, and 6. A summary of these applications is given in research outcome 5.

7.3 Recommendations for future research and applications

This research has involved a range of aspects of GBSAR interferometry and produced a complete in-house software package (see Appendix B) for deformation monitoring. Additional research effort is now needed to further improve the performance of the developed package and exploit its value in geohazard monitoring and structural deformation surveying. The following work could be considered to add value in the future.

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1. Automatic correction of phase unwrapping errors

The detection of phase unwrapping errors has been integrated into the developed package. However, the automatic correction of unwrapping errors has not been achieved, and would represent a valuable topic for future work. Although several previous studies in both spaceborne and ground-based SAR (e.g. Biggs et al., 2007; Crosetto et al., 2011; López-Quiroz et al., 2009; Monserrat et al., 2009; Zhao et al., 2016) attempted to address this issue, these approaches perform pixel-wise correction of unwrapping errors in post-processing, and generally require visual inspection (Biggs et al., 2007). Unwrapping errors usually present regional patterns (Biggs et al., 2007), and the accurate identification of regional unwrapping errors is required. In the case that unwrapping errors are detected, RT-GBSAR requires the fully automatic correction of unwrapping errors to be achieved in real time.

2. Graphical processing unit (GPU) acceleration

The whole data processing package has been developed using MATLAB release 2016b (The MathWorks, Inc.), with some code converted into C++. The entire program is currently based on central processing unit computation. To meet the increasing requirements associated with the advancement of GBSAR hardware, especially the ground-based MIMO radar (or MIMO- SAR) which is potentially capable of generating a number of images per second, the real-time capability of this package should be enhanced, possibly via high-performance computational techniques such as GPU acceleration (e.g. Reza et al., 2018; Zhang et al., 2014).

3. 1D (LOS) measurements to 3D measurements

Like other InSAR techniques, GBSAR interferometry provides 1D surface displacements along the LOS direction. In comparison to 3D measurements, 1D LOS displacements may be insufficient to interpret some of the processes behind observations (e.g. Caduff et al., 2015; Kristensen et al., 2013). To achieve 3D measurements, GBSAR observation can be performed from multiple stations, which is similar to the concept of multiple geometries in spaceborne InSAR (e.g. Hu et al., 2012; Wright et al., 2004). Alternative strategies could include prior knowledge (or assumption) about the displacement direction (Caduff et al., 2015) and integration with other measurements, such as GNSS, TLS, and spaceborne InSAR (e.g. Bardi et al., 2016; Kristensen et al., 2013; Rödelsperger et al., 2010).

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Although all of the applications presented in this research are short-term cases, the developed software package is actually ready for both short- and long-term deformation monitoring applications. Long-term monitoring cases may require extra effort in hardware deployment and management. In terms of data acquisition, it can be carried out through long-term continuous operation or multi-campaign discontinuous operation. Data acquisition in any operation mode can be processed by the developed package together with RT-GBSAR and MC-GBSAR chains. It should be noted that in the long-term monitoring of a natural slope with thick vegetation coverage, temporal decorrelations can be serious, thus constraining the feasibility of GBSAR interferometric measurement. The use of corner reflectors may be beneficial in such cases (Crosetto et al., 2014a).

5. Early warning systems for landslides and infrastructure failures

Early warning systems work as risk mitigation tools by calling for actions in specific circumstances and in areas where hazard risk goes beyond a tolerable level (Calvello, 2017). Apart from monitoring, an efficient landslide early warning system also comprises analysis and forecasting, warning, and response elements (Intrieri et al., 2012). GBSAR interferometry has been increasingly adopted to implement landslide early warning systems (e.g. Atzeni et al., 2015; Casagli et al., 2010; Intrieri et al., 2012). Future effort should be made on combining the proposed GBSAR interferometric framework with appropriate forecasting, warning, and response to implement a more effective landslide early warning system. In addition, future work also includes exploiting the GBSAR monitoring of structural deformation for dams, levees, embankments, and other infrastructure, in order to effectively analyse abnormal behaviour that may threaten the safety of the structures, implement maintenance and remedial measures, and predict potential failures.

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Appendix A: Inversion precision

The goal of InSAR time series analysis for deformation monitoring is to obtain the deformation time series. The mean velocity between time-adjacent acquisitions is a preferred choice in InSAR time series analysis to avoid large discontinuities in cumulative deformations and to obtain a physically sound solution (e.g. Berardino et al., 2002; Li et al., 2009). Accordingly, the prerequisite is to obtain the incremental time series of phase change between time-adjacent acquisitions. We assume a redundant network of L interferograms formed by N SLC images. Each pixel is associated with a system in the following matrix representation:

𝐁𝐿×𝑁 𝚽𝑁×1 = 𝛅𝚽𝐿×1+ 𝛆𝐿×1, (A.1)

where 𝐁 is the coefficient matrix; 𝚽 is the matrix containing the incremental time series of phase change with respect to the superposition of both displacement and atmospheric variation; 𝛅𝚽 is the matrix of redundant unwrapped interferometric phase; 𝛆 is the noise matrix. With redundant interferometric phase, the optimal estimation of the incremental time series of phase change 𝚽̂ for each pixel can be performed based on equation (A.1) via any appropriate solvers (e.g. singular value decomposition, normal least squares). The phase residuals in the inversion are:

𝐕𝐿×1= 𝐁𝐿×𝑁 𝚽̂𝑁×1− 𝛅𝚽𝐿×1. (A.2)

The root mean square of phase residuals for a pixel is:

𝜎₀ = √𝐕T_𝑟𝐕= √_{𝑛−𝑁+1}𝐕T𝐕 , (A.3) where 𝑟 is the number of redundancies and 𝑛 is the number of coherence occurrences in the redundant network. Accordingly, the covariance matrix of the estimated 𝚽̂𝑁×1 can be

calculated by:

D_{𝚽̂ 𝚽}̂ = 𝜎0√(𝐁T𝐁)−1. (A.4)

As the final cumulative displacement is obtained by removing atmospheric variation from the sum of them, we introduce an estimator 𝑑̂ which is the sum of the cumulative displacement and atmospheric variation between the first image and the last image:

152 𝑑̂ = −_4𝜋𝜆 ∑ (𝜑̂_𝑡𝑑𝑖𝑠_{𝑘𝑡𝑘+1+ 𝜑̂} 𝑡𝑘𝑡𝑘+1 𝑎𝑡𝑚 ₎ 𝑁−1 𝑘=0 = 𝐅1×𝑁𝚽̂𝑁×1, (A.5)

where 𝐅 = [− 𝜆 4𝜋⁄ ⋯ − 𝜆 4𝜋⁄ ] . The theoretical precision of d̂ is used as the precision indicator in the estimation for each pixel, which is calculated by:

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Appendix B: Ground-based Synthetic Aperture Radar Interferometry

Software (GBSAR-InS)

Ground-based Synthetic Aperture Radar Interferometry Software (GBSAR-InS) is a GBSAR data processing software package for deformation monitoring developed by the author. The relevant InSAR algorithms, processing strategies described in this thesis have been implemented and integrated into GBSAR-InS. The software package is able to process GBSAR data acquired in any operation modes and therefore supports both continuous and discontinuous GBSAR monitoring, and it was used to generate the results shown in this thesis. The notable features of GBSAR-InS are highlighted as follows:

(1) A fully automatic chain, RT-GBSAR presented in Chapter 5, has been developed and integrated into GBSAR-InS for the (near-) real-time processing of continuous GBSAR data. RT-GBSAR possesses three features: (i) low requirement of computational memory; (ii) insights into the temporal evolution of surface movements through temporally-coherent pixels; and (iii) (near-) real-time capability of processing an infinite number of images.

(2) Another fully automatic chain, MC-GBSAR presented in Chapter 6, has been developed and integrated into GBSAR-InS for processing discontinuous multi- campaign GBSAR data. In MC-GBSAR, (i) images from different campaigns with repositioning errors can be automatically co-registered; and (ii) atmospheric, geometric, and topographic errors can be corrected in a single step without any additional materials or a-priori knowledge.

(3) GBSAR-InS uses advanced InSAR techniques in every processing step, including (i) the non-local “MIAS” method, presented in Chapter 3, for accurate coherence estimation and phase filtering; and (ii) the approach to selecting fully and partially coherent pixels, which is presented in Chapter 4.

(4) GBSAR-InS provides user interfaces for data management and data visualisation. The package is able to output cumulative displacement maps, deformation velocity maps, atmospheric and/or repositioning error maps between any two epochs, as well as the line graph of time-series displacement for every coherent pixel. It is also able to output precision maps and unwrapping error maps to assess the reliability of InSAR

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GBSAR-InS was developed based on Matlab release 2016b software. The data processing of GBSAR-InS starts with focused single-look complex images, and it uses SNAPHU (https://web.stanford.edu/group/radar/softwareandlinks/sw/snaphu/, accessed: 08 December, 2018) for 2D phase unwrapping and partial StaMPS unwrapping source codes (https://homepages.see.leeds.ac.uk/~earahoo/stamps/, accessed on 08 December, 2018) for 3D phase unwrapping. Using the continuous GBSAR dataset (i.e. Dataset I), Figures B.1 to B.6 show the key user interfaces and outputs of GBSAR-InS.

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Figure B.2. The user interface for cumulative displacement map plotting.

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Figure B.4. The user interface for examining phase unwrapping errors.

Figure B.5. Cumulative displacement map (the left one) and line graphs of displacement and error time series (the right two).

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